Prove that for each natural it's
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Use proof by induction
(I): Let n=2
and on 1<x<2, , so the above integral is .
(II): Assume that for n.
Using the fact that for n<x<n+1 in the rightmost integral,
And we have our proof.
i was about to give the same proof.. but i can't fix the latex.. haha
We have hence finally
And we're done!
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